nnvolterra

Run Code

Compile first: make compile

Run all codes: make all

Test xconv: make npxconv_test

MNIST dataset needs to be downloaded, converted to numpy format, and placed to mnist/ folder.

Train MNIST network: make mnist_train

Test MNIST network: make mnist_try

Hack MNIST network: make mnist_hack

Required

• python
• numpy
• pytorch
• g++ 9.3.0
• xelatex [optional]: for mnist_draw.py

About Files

• xconvlibrary
  • xconvolution.hpp: core lib
  • npxconv.cpp: cpp to python
  • npxconv.py: interface for python
  • npxconv_setup.py: setup
  • npxconv_test.py: test file
• outer convolution
  • oconv_draw.py: nnfragile and three example images of outer convolution
  • oconv_rank.py: compute rank for outer convolution and neural network to Volterra Convolution
  • oconv_rank_draw.py: draw images from oconv_rank.py
• mnist hack
  • mnist_module.py: the module
  • mnist_train.py: train this module in training set
  • mnist_try.py: check module in test set
  • mnist_hack.py: try to hack the module
  • mnist_draw.py: slightly draw the hack result
• other
  • tensordec.py: about tensor decomposition
  • shape_check.py: check shapes

Please Cite

@misc{li2021understanding,
      title={Understanding Convolutional Neural Networks from Theoretical Perspective via Volterra Convolution}, 
      author={Tenghui Li and Guoxu Zhou and Yuning Qiu and Qibin Zhao},
      year={2021},
      eprint={2110.09902},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}